In the pane on Differential Forms of the menu “Books”, one can find the second chapter minus references of a book on the exterior calculus of scalar-valued differential forms. That book is the first one in a series of four books on mathematics for physicists, mathematicians and engineers by Jose G. Vargas. In the opinion of the author, the education of theoretical physicists in mathematics is awfully inadequate, and the education of most mathematicians is very shallow in matters of differential geometry and advanced modern calculus. When it is not shallow, it is unnecessarily cumbersome and complicated.
This series will try to correct that. It will be an (Élie) Cartan-Kähler-Clifton festival. Readers can find about Cartan and Kähler in the web. As for Clifton, he made rigorous Cartan’s approach to differential geometry without corrupting it; he added to the highly intuitive theory of the moving frames just a few definitions and theorems. Nothing else was needed.
In order to carry out this program, a lot of encouragement and feedback will be needed. One day, other mathematicians or mathematical physicists might wish to add their own contribution to newer versions of the books, in order to increase the amount of advanced but no too excedingly specialized mathematics that one can do with differential forms. If you like the spirit of chapter 2 and the preprints, and have constructive comments or suggestions, please let the author know in the email buttons to the right. I shall try to answer everybody, though can not promise.
Jose Vargas and Doug Torr will make every effort to respond to questions on their papers and the subject of Cartan-Kähler Unification.